1

Autonomous Ground Vehicle Path Planning in

Urban Environments using GNSS and Cellular

Signals Reliability Maps: Simulation and

Experimental ResultsSonya Ragothaman, Student Member, IEEE, Mahdi Maaref,

and Zaher M. Kassas, Senior Member, IEEE

Abstract—A framework for autonomous ground vehicle (AGV)path planning using global navigation satellite systems (GNSS)signals and cellular long term evolution (LTE) signals is evaluatedthrough several simulations and experiments. The objective ofpath planning is to prescribe the optimal path for the AGV tofollow to reach a desired target point. Optimality is defined as theshortest distance, while minimizing the AGV’s position estimationerror and guaranteeing that the uncertainty about its positionis below a desired threshold. Path planning is prescribed viasignal reliability maps, which provide information about regionswhere large errors due to cellular signal multipath or obstructedGNSS line-of-sight are expected. Simulation results are presenteddemonstrating that utilizing ambient cellular LTE signals to-gether with GNSS signals (1) reduces the uncertainty about theAGV’s position, (2) increases the number of feasible paths tochoose from, which could be useful if other considerations arise(e.g., traffic jams and road blockages due to construction), and (3)yields significantly shorter feasible paths, which would otherwisebe infeasible with GNSS signals alone. Experimental results ona ground vehicle navigating in downtown Riverside, California,USA, are presented demonstrating a close match between thesimulated and experimental results.

Keywords—Path planning, ground vehicles, cellular signals,GNSS, geographic information systems (GIS).

I. INTRODUCTION

To ensure safe and efficient operation of future autonomous

ground vehicles (AGVs), one must establish performance

guarantees prior to their deployment into the environment.

These performance guarantees consider the AGV’s sensing and

computation capabilities as well as environmental factors (e.g.,

road map, traffic, weather, time of day, etc.). Issues pertain-

ing to perception, navigation, and control of AGVs become

increasingly coupled [1], [2]. In this respect, an AGV could

plan its path, which may temporarily detract it from its desired

final destination, in exchange for improving its situational

awareness and guaranteeing desired safety measures [3].

This paper considers the following problem, originally de-

fined in [4], [5]. An AGV is equipped with receivers capable

This work was supported in part by the Office of Naval Research (ONR)under Grant N00014-16-1-2809 and in part by the National Science Founda-tion (NSF) under Grants 1929571 and 1929965.

S. Ragothaman was with the University of California, Riverside and isnow with The Aerospace Corporation. M. Maaref and Z. Kassas are withthe Department of Mechanical and Aerospace Engineering, The Universityof California, Irvine. (email: srago001@ucr.edu, mmaaref@uci.edu,and zkassas@ieee.org).

of producing pseudoranges to overhead GNSS satellites (e.g.,

[6]–[9]) and to cellular long-term evolution (LTE) base stations

in its environment (e.g., [10]–[13]). The AGV fuses these

pseudoranges to estimate its position and clock bias. The AGV

is also equipped with a three-dimensional (3-D) building map

of the environment (e.g., [14], [15]). Starting from a known

point, the AGV desires to reach a target point by taking the

shortest path, while minimizing the AGV’s position estimation

error and guaranteeing that the uncertainty about its poisition

is below a desired threshold. Towards this objective, a signal

reliability map is first generated that specifies which signals

are reliable to use at different locations and at different times

in the environment. Each point in the environment has a

corresponding signal reliability (a boolean measure) for the

different overhead GNSS satellites and nearby cellular base

stations. A reliable GNSS satellite means that there exists an

unobstructed line-of-sight (LOS) to that satellite. A reliable

cellular base station means that the pseudorange bias due

to multipath is below a certain threshold. Next, equipped

with this signal reliability map, a path planning generator

produces (i) the optimal path to the target point, if any, and (ii)

other feasible paths the AGV could take. These suboptimal,

yet feasible paths could be useful, should the AGV choose

to not follow the optimal path, e.g., to avoid traffic jams

and road blockages due to construction or emergency. A

table specifying the reliable GNSS satellites and cellular base

stations to use along the optimal and feasible paths is also

generated. Two path planning algorithms are considered: one

which is suitable for short travel times and assumes that the

GNSS satellite geometry is fixed, while the other is suitable

for long travel times and considers GNSS satellite motion.

The second algorithm is more computationally involved. The

prequel of this paper surveyed related work and presented

relevant models, analytical derivations, and algorithm develop-

ment [5]. This paper presents comprehensive simulation and

experimental studies for different realistic scenarios to evaluate

the accuracy and efficacy of the proposed approach on an AGV

navigating in a deep urban environment.

This paper is organized as follows. Section II gives an

overview of the different driving scenarios considered in this

paper. Sections III and IV present simulation and experimen-

tal results evaluating the performance of the path planning

approach, respectively. Section V gives concluding remarks.

Preprint of article accepted for publication in IEEE Transactions on Aerospace and Electronic Systems

II. SCENARIOS OVERVIEW

The simulation study considers three different AGV driving

scenarios, in which

• Scenarios 1 and 2 compare the feasible paths for two

AGVs, where one of the AGVs does not use cellular LTE

signals to produce an estimate of its state (i.e., the AGV

only uses GNSS signals). These scenarios demonstrate

that utilizing the freely available cellular signals in the

environment for AGV navigation: (i) reduces the position

estimation error and (ii) increases the number of feasible

paths to the target point.

• Scenario 3 compares the two path planning algorithms

which (i) assume fixed GNSS satellite geometry and (ii)

consider GNSS satellite motion, for a long travel time

(long trajectory). This scenario demonstrates the effect

of satellite motion on the performance of each of the

algorithms.

• Scenario 4 considers different combinations of receivers:

GPS only, GPS + cellular, GPS + Galileo, and GPS +

Galileo + cellular, to study the impact of adding different

types of signals.

The experimental study was conducted on a ground vehicle

driving in downtown Riverside, California, USA, using real

GPS and LTE signals. Three driving scenarios are considered,

in which

• Scenario 1 compares the experimental navigation per-

formance with the performance simulated by the path

planning generator. A close match is demonstrated be-

tween the optimal path generated experimentally and in

simulation.

• Scenario 2 evaluates the navigation performance when the

vehicle traverses the shortest path, which is an infeasible

path according to the path planning generator. This sce-

nario demonstrates that the path planning generator was

able to predict poor (unsafe) navigation performance.

• Scenario 3 considers long travel time (long trajectory)

and compares the two path planning approaches which (i)

assume fixed GNSS satellite geometry and (ii) consider

GNSS satellite motion. This scenario demonstrates an

improved navigation performance in the path planning

generator that accounts for GNSS satellite motion.

The significance of the proposed AGV path planning frame-

work is threefold and is clearly demonstrated in the simulation

and experimental results herein. First, it is shown that using

cellular signals in the environment “opens up” new areas

to navigate reliably and safely, which were infeasible with

GNSS only. This alleviates the need to equip the vehicle

with additional high-grade sensors that may violate cost, size,

weight, and power (C-SWaP) constraints. Second, it is shown

that the proposed approach can successfully predict whether

the AGV’s paths satisfy or violate a desired position estimation

uncertainty. This is crucial for safety considerations as the

shortest (or some other path) may not be safe to traverse.

Third, the optimal path accounts for both distance and position

mean-squared error (MSE) to ensure that lengthy, yet safe

paths (e.g., paths that require the AGV to leave and re-enter

the urban environment) are deweighted.

III. SIMULATION STUDY

This section presents simulation results evaluating the per-

formance of the path planning approach developed in [5].

A. Simulation Environment Setup

The simulation environment considered an AGV navigating

downtown in Riverside, California, USA. A 3-D building

map of this environment was obtained from ArcGIS [16].

The GNSS satellite constellations comprised GPS and Galileo

satellites. Fig. 1 illustrates the GNSS satellites’ skyplot over

Riverside at time t = 11:00 am, coordinated universal time

(UTC), on August 23, 2018. The elevation and azimuth angles

for both GPS and Galileo satellites were obtained using the

PyEphem Python library [17]. Satellites with an elevation

angle less than 15◦ were not used, as signals from these

satellites tend to be severely degraded due to ionosphere,

troposphere, and multipath [18].

GPS

Galileo

N

NW

W

S

E

SW SE

20

18

7

30

8

2

31

10

32

1126

122

14

Fig. 1. Skyplot showing elevation and azimuth angles of GNSS satellites overRiverside, California, USA, at 11:00 am UTC, August 23, 2018. The numberscorrespond to the pseudorandom noise (PRN) code for each GPS and Galileosatellite [19], [20]. Data source: [21].

Fig. 2 illustrates the simulation environment. The simulation

settings for all four scenarios are summarized in Table I.

Start point

Target point

Cellular Tower

200 mCellular tower 2

Cellular tower 1

Cellular tower 4

Cellular tower 3

Fig. 2. Simulation environment showing start and target points and locationof cellular base stations. This figure was obtained with ArcGIS® [14].

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Preprint of article accepted for publication in IEEE Transactions on Aerospace and Electronic Systems

TABLE ISIMULATION SETTINGS

Parameter Definition Value

N Number of GNSS satellites 14

MNumber of cellular base

stations4

t Time in UTC (Scenario 1 & 2)August 23, 2018,

11:00 am

{σ2gnss,n}Nn=1

GNSS measurement noisevariance

5 m2

{σ2cell,m

}Mm=1

Cellular measurement noisevariance

5 m2

X Number of impulsesAn output of

Wireless Insite

ai(x)Complex amplitude of signal

path x and LTE symbol iAn output of

Wireless Insite

τi(x)Path delay between the x-th

impulse to the LOS pathAn output of

Wireless Insite

Ts Sampling interval 3.25 × 10−8 s

LNumber of subcarrier symbols

in the pilot sequence200

ξCorrelator spacing in the LTE

receiver tracking loop0.5

eθ Symbol timing error 0

B. GNSS Simulation

GNSS signal reliability map were generated. The GNSS

satellite ephemeris data was found on the North American

Aerospace Defense Command (NORAD) two-line element

data set [22]. A 3-D building map was obtained from ArcGIS®.

The accuracy of the map is expected to be around 4.13 m based

on a study of OpenStreetMap [16], [23]. A Python toolbox in

ArcGIS® was created to generate point features with reliability

map information for a specified time interval. GNSS LOS was

calculated by generating a line feature of fixed length along

the LOS between the GNSS satellite and the point feature

location. GNSS LOS was calculated at 5-second intervals, and

times with changed visibility were recorded as tuples.

C. Multipath Simulation

Pseudorange biases caused by multipath were simulated.

The complex channel impulse responses on a grid of receiver

locations were generated using Wireless Insite X3D model

[24] to calculate multipath bias bm,p according

bm,p , χm + cτi(0)− dLOS, m = 1, . . . ,M, (1)

for each receiver location index p. In (1):

• c is the speed of light

• dLOS is the length of the LOS path and is equal to the

distance between the receiver and the transmitter in each

simulated receiver location.

• τi(0) is the time of flight of the first received peak and

is an output of Wireless Insite.

• χm is the multipath interference bias, calculated from

equations (7) and (8) in [5]. The parameters to construct

χm are given in Table I, among which X , ai(x), and

τi(x) are outputs of Wireless Insite.

The simulated induced multipath biases {bm,p}4m=1 obtained

from (1) for all four transmitters and {pi}1000i=1 receiver lo-

cations with a spacing of 8 m are shown in Fig. 3. It is

worth noting that the path planning generator evaluates the

position MSE calculated using the LTE measurement variance

and multipath-induced biases, but does not generate simulated

LTE pseudorange measurements.

0 200 400 600 800 1000

Receiver location indices

-2

0

2

4

6

Multip

ath

bia

s [m

]

Tower 2

0 200 400 600 800 1000

Receiver location indices

-4

-2

0

2

4

6

Multip

ath

bia

s [m

]

Tower 3

0 200 400 600 800 1000

Receiver location indices

-5

0

5

Multip

ath

bia

s [m

]

Tower 4

0 200 400 600 800 1000

Receiver location indices

-5

0

5

Multip

ath

bia

s [m

]

Tower 1

Fig. 3. The simulated induced multipath bias for all cellular base stationsobtained from (1).

D. Simulation Scenario Description

The output of the path planning generator is studied over

four scenarios. In the first two scenarios, two AGVs were

considered with the same start and target positions and time of

departure. The optimization problem for each AGV used the

same threshold values λmax and rmax. The optimal and feasi-

ble paths for both vehicles were calculated using Approach A

described in [5], which does not account for GNSS satellite

motion. AGV A was equipped with only GPS and Galileo

receivers, while AGV B was equipped with GPS, Galileo, and

cellular LTE receivers. The receiver clocks were synchronized

for each vehicle, and the appropriate matrix B was used (see

Equation (5) in [5]).

In the third scenario, an AGV was equipped with GPS,

Galileo, and cellular LTE receivers. The AGV was prescribed

a long trajectory, with different start and target locations from

the first two scenarios. A trajectory is considered long if it

is expected to take longer than 15 minutes to traverse, or if

there is a sharp change in the GNSS LOS along the path.

The optimal and feasible paths were calculated using: (i)

Approach A: does not account for GNSS satellite motion and

(ii) Approach B: accounts for GNSS satellite motion [5].

In the fourth scenario, four receiver combinations were

considered: (i) GPS only, (ii) GPS + cellular, (iii) GPS +

Galileo, and (iv) GPS + Galileo + cellular. The position RMSE

and maximum eigenvalue metrics were calculated over a few

locations to analyze the impact of adding receivers to the

simulated positioning accuracy.

E. Simulation Results

1) Scenario 1: Table II shows the thresholds used for

both AGV A and AGV B. The user-specified thresholds are

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rmax and λmax, from which ηmax is computed according to

equation (16) in [5], and ηm corresponds to the m-th element

of R−T

a 1(N+M)×1ηmax. The thresholds were chosen such that

rmax +√λmax is approximately half the width of the street.

The thresholds were chosen to bound the error statistics such

that the vehicle does not calculate position to be in the middle

of a building or at a different location index further up the

street. It is important to know the correct closest location index

because the set of reliable transmitters is different for each

location index. Using the reliable transmitters at an adjacent

location index can cause the AGV-mounted receiver to use

measurements that are not reliable.

TABLE IISCENARIO 1 THRESHOLDS

Parameter Definition Value

rmax Position bias threshold 4 m

λmaxEigenvalue constraint

threshold4 m2

ηmax Pseudorange error threshold 1 m

ηmWeighted pseudorange error

threshold

√5 m

For the given simulation settings, AGV A had no feasible

path which satisfies the constraints. One path was returned

by the the path planning generator by relaxing the eigenvalue

constraint to λmax = 4.44 m2. Fig. 4 (a) illustrates this path.

Table III presents this path’s distance, total RMSE, maximum

eigenvalue, and the cost function value (see Equation (12) in

[5] for optimization problem). For a given path π, the total

RMSE was calculated according to

Total RMSE =

√√√√∑p∈π

MSE(p)

h(π),

where h(·) denotes the number of locations in path π. In

contrast, AGV B had four feasible paths without the need to

relax the eigenvalue constraint (i.e., with λmax = 4), with Path

B1 being the optimal path. Fig. 4 (b) illustrates these paths and

Table III compares them.

TABLE IIISCENARIO 1 RESULTS

Path DistanceTotal

RMSEMaximumeigenvalue

Cost

function

value

AGV A Path A1⋆ 1006 m 4.37 m 4.44 m2 16397

AGV B Path B1 995 m 3.91 m 3.53 m2 13108

Path B2 1016 m 3.91 m 3.74 m2 13158

Path B3 1006 m 3.95 m 3.91 m2 13358

Path B4 1004 m 3.96 m 3.74 m2 13408

⋆ No feasible path was found for AGV A. This path was found after

relaxing the the eigenvalue constraint.

The following can be concluded. First, including cellular

LTE signals made the optimization problem feasible, without

having to relax the constraint. Second, including cellular LTE

signals resulted in several feasible paths to choose from

(besides the optimal path), which could be useful if other

considerations arise. Third, while the optimal path ended up

yielding the shortest distance together with the total RMSE, a

tradeoff between the shortest path and the total RMSE can be

seen in the other feasible paths (e.g., Path B2 has lower total

RMSE than Path B3 but has longer distance).

Target point

Start point Path A1: optimal

(a) (b)

Path B1: optimalPath B2: feasiblePath B3: feasiblePath B4: feasible

Fig. 4. Simulation results for Scenario 1. (a) The optimal path for AGVA, generated after relaxing the eigenvalue constraint from λmax = 4 toλmax = 4.44. (b) The optimal path and three feasible paths for AGV Bwithout relaxing the eigenvalue constraint (i.e., with λmax = 4). The optimalpath Path B1 was shorter and produced less total RMSE than all other paths:Path A1, B2, B3, and B4. This figure was obtained with ArcGIS® [14].

2) Scenario 2: This scenario is similar to Scenario 1, except

that the eigenvalue constraint is relaxed even further to obtain

several feasible paths for AGV A. Table IV shows the new

thresholds used for both AGV A and AGV B.

TABLE IVSCENARIO 2 THRESHOLDS

Parameter Definition Value

rmax Position bias threshold 4 m

λmaxEigenvalue constraint

threshold5 m2

ηmax Pseudorange error threshold 2√

5m

ηmWeighted pseudorange error

threshold2 m

By changing the constraints from Scenario 1, the number of

feasible paths for AGV A increased from zero to two, while

for AGV B they increased from 4 to 12. Fig. 5 illustrates these

paths and Table V compares them.

The following can be concluded. First, while both AGV

A and AGV B found optimal and feasible paths, the optimal

path for AGV B was significantly shorter than that for AGV

A. Hence, utilizing cellular signals “opened up” areas in the

environment that were otherwise infeasible with GNSS only.

Second, slightly relaxing the constraint resulted in many new

feasible paths versus Scenario 1, with the optimal path Path B1

in Scenario 2 being reasonably shorter than the optimal path

in Scenario 1 (namely, 33% shorter) with a slightly larger

RMSE (namely, 11% higher). It should be noted that in a

realistic scenario, if the designer found that there would be

no feasible paths for the vehicle, a receiver for another GNSS

constellation (or additional sensors) can be added, instead of

adjusting the constraints.

3) Scenario 3: Table II and Table VI show the simulation

settings for this scenario. The simulation settings were chosen

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TABLE VSCENARIO 2 RESULTS

Path DistanceTotal

RMSE

Maximum

eigenvalue

Costfunction

value

AGV A Path A1 1006 m 4.37 m 4.44 m2 16397

Path A2 1013 m 4.44 m 4.44 m2 17012

AGV B Path B1 748 m 4.34 m 4.28 m2 11724

Path B2 995 m 3.91 m 3.53 m2 13108

Path B3 1016 m 3.91 m 3.74 m2 13158

Path B4 1006 m 3.95 m 3.74 m2 13358

Path B5 1004 m 3.95 m 3.74 m2 13408

Path B6 1013 m 3.97 m 4.28 m2 13412

Path B7 1006 m 3.97 m 4.28 m2 13462

Path B8 1014 m 4.17 m 4.28 m2 14605

Path B9 1493 m 4.08 m 4.20 m2 21519

Path B10 1491 m 4.18 m 4.28 m2 22515

Path B11 1750 m 4.11 m 4.28 m2 24401

Path B12 1756 m 4.11 m 4.28 m2 25397

Target point

Start point

Path A1: optimalPath A2: feasible

Path B1: optimalPath B2: feasiblePath B3: feasiblePath B4: feasible

Path B5: feasiblePath B6: feasiblePath B7: feasiblePath B8: feasible

Path B9: feasiblePath B10: feasiblePath B11: feasiblePath B12: feasible

(b)(a)

(d)(c)

Fig. 5. Simulation results for Scenario 2. (a) The feasible paths for AGV A,where Path A1 is the optimal path. (b) Four feasible paths for AGV B whichproduced the lowest cost function, i.e., Paths B1 – B4. (c) Paths B5 – B8 forAGV B in order of lowest to highest cost function value. (d) Paths B9 – B12for AGV B in order of lowest to highest cost function value. This figure wasobtained with ArcGIS® [14].

at a time when there were sharp changes in the costs and

constraints over the duration of the AGV’s trajectory due to

GNSS satellite motion. The value ζ was chosen such that

the search space for Approach B included all paths that were

feasible using Approach A.

For the given simulation settings, there are eight feasible

paths according to Approach A, and 279 feasible paths ac-

cording to Approach B. Fig. 6 shows the first eight feasible

TABLE VISCENARIO 3 SETTINGS

Parameter Definition Value

t Time in UTCDecember 26, 2018,

3:04 pm

vAGV Vehicle speed 3.2 m/s

ζSearch space size for path

planning generator4534

paths using either approach and Table VII compares them.

TABLE VIISCENARIO 3 RESULTS

Path DistanceTotal

RMSE

Maximum

eigenvalue

Cost

function

value

ApproachA

Path A1 1600 m 2.97 m 3.22 m2 14934

Path A2 1603 m 2.97 m 3.22 m2 15029

Path A3 1862 m 2.94 m 2.90 m2 17042

Path A4 1865 m 2.94 m 2.90 m2 17137

Path A5 1854 m 2.97 m 3.22 m2 17190

Path A6 1857 m 2.97 m 3.22 m2 17285

Path A7 2116 m 2.94 m 2.90 m2 19298

Path A8 2119 m 2.94 m 2.90 m2 19393

ApproachB

Path B1 1605 m 2.84 m 3.55 m2 12336

Path B2 1608 m 2.84 m 3.55 m2 12526

Path B3 1609 m 2.82 m 3.55 m2 13165

Path B4 1612 m 2.83 m 3.55 m2 13345

Path B5 1864 m 2.76 m 3.69 m2 13829

Path B6 1855 m 2.80 m 3.69 m2 13831

Path B7 1854 m 2.83 m 3.69 m2 13861

Path B8 1863 m 2.79 m 3.69 m2 13866

The following can be concluded. First, new feasible paths

became available in Approach B. There were 48 feasible paths

with lower cost than Path A1. This occurred because after the

start time, there was a significant decrease in the maximum

eigenvalue in several areas in the road network, which resulted

in a large increase in the number of feasible paths. Clearly,

there was large discrepancy between the simulation results

of both approaches, which demonstrates that accounting for

satellite motion is necessary for long trajectories. Second, there

were feasible paths according to Approach A that were in

fact infeasible, e.g., Paths A1 (the optimal path), A2, A5, and

A6. An AGV that takes any of these paths will suffer from a

navigation performance violating the desired constraints. Even

if the optimal path for Approach A was the same as that of

Approach B, the table of reliable GNSS satellites and cellular

base stations produced by Approach A does not account for

satellite motion and may become unusable as GNSS satellites’

LOS geometry change over long durations. This may cause the

AGV to ignore measurements that are in fact reliable, or accept

measurements that are unreliable. This result demonstrates

the importance of accounting for satellite motion for long

trajectories.

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(a) (b)

(c) (d)

Target point

Start point

Path A1: optimalPath A2: feasiblePath A3: feasiblePath A4: feasible

Path A5: feasiblePath A6: feasiblePath A7: feasiblePath A8: feasible

Path B1: optimalPath B2: feasiblePath B3: feasiblePath B4: feasible

Path B5: feasiblePath B6: feasiblePath B7: feasiblePath B8: feasible

Fig. 6. Simulation results for Scenario 3. (a) Four feasible paths fromApproach A which produced the lowest cost function, i.e., Paths A1 – A4. (b)Paths A5 – A8 from Approach A in order of lowest to highest cost functionvalue. (c) Paths B1 – B4 from Approach B in order of lowest to highest costfunction value. (d) Paths B5 – B8 from Approach B in order of lowest tohighest cost function value. This figure was obtained with ArcGIS® [14].

4) Scenario 4: This scenario compares four receiver com-

binations (i) GPS only, (ii) GPS + cellular, (iii) GPS +

Galileo, and (iv) GPS + Galileo + cellular. The position RMSE

and maximum eigenvalue metrics are calculated over a few

locations to demonstrate the impact of adding receivers to the

expected positioning accuracy. The path planning metrics are

calculated using the simulation settings in Table IV. Fig. 7

shows the position RMSE and maximum eigenvalue metrics.

Based on Fig. 7, it is obvious that using receivers (i) and (iv)

is expected to yield the worst and best navigation performance,

respectively. This can be seen based on both the position

RMSE and eigenvalue constraint metrics. The RMSE with

receiver (iii) was lower than (ii) in some locations. This result

is expected because more Galileo satellites than cellular base

stations were present (namely, 7 versus 4). However, there

are some locations where receiver (ii) outperforms than (iii).

This is especially true for the maximum eigenvalue metric,

which corresponds to the maximum position uncertainty and

the upper bound on the position bias. It can be seen that there

is one location where the maximum eigenvalue constraint is

satisfied for (ii), but not for (iii). This shows that although (iii)

performs better than (ii) for many locations, there are some

locations that using cellular signals can “open up” areas in the

environment that were otherwise infeasible with GNSS only.

IV. EXPERIMENTAL STUDY

This section presents experimental results for ground vehicle

path planning in an urban environment with real GPS and

cellular LTE signals.

(a)

(c)

(e)

(g)

RMSE < 5

5<RMSE<10

10<RMSE<15

RMSE > 15

N=A

(b)

(d)

(f)

(h)

3 < λmax < 3:53:5 < λmax < 44 < λmax < 4:5

N=A

λmax < 3

4:5 < λmax < 5

(i) GPS only

(ii) GPS +cellular

(iii) GPS +Galileo

(iv) GPS +

Galileocellular +

Position RMSE λmax constraint

Fig. 7. Simulation results for Scenario 4. The shown receiver combinationsare (a)–(b) GPS only, (c)–(d) GPS + cellular, (e)–(f) GPS + Galileo, and (g)–(h) GPS + Galileo + cellular. The left column (a), (c), (e), (g) correspondsto simulated position RMSE. The right column (b), (d), (f), (h) correspondsto the simulated largest eigenvalue metric. N/A corresponds to the situationin which the vehicle-mounted receiver did not have a sufficient number ofmeasurements to estimate the vehicle’s position. This figure was obtainedwith ArcGIS® [14].

A. Experimental Setup and Scenario Description

A vehicle is equipped with two consumer-grade omnidi-

rectional Laird antennas [25] to receive cellular LTE signals

at two frequencies specified in Table VIII. The vehicle’s

position is taken as the midpoint of the antennas. The cel-

lular LTE signals were down-mixed and sampled using a

National Instruments (NI) dual-channel universal software

radio peripheral (USRP)–2954R®, driven by a GPS-disciplined

oscillator (GPSDO) [26]. The vehicle was also equipped

with a Septentrio AsteRx-i V® integrated GNSS and inertial

measurement unit (IMU) module, which is equipped with a

dual antenna, multi-frequency GNSS receiver, and a Vector-

nav VN-100 micro-electromechanical system (MEMS) IMU.

Septentrio’s post-processing software development kit (PP-

SDK) was used to process carrier phase observables collected

by the AsteRx-i V® and by a nearby differential GPS base

station to obtain a carrier phase-based navigation solution. This

integrated GNSS-IMU real-time kinematic (RTK) system was

used to produce the vehicle’s ground truth path. The GNSS

receiver also produced GPS pseudorange measurements. Cel-

lular LTE pseudoranges measurements were produced with the

Multi-channel Adaptive TRansceiver Information eXtractor

(MATRIX) software-defined receiver (SDR) [13], [27]. The

experimental setup is shown in Fig. 8.

The experiment was conducted in downtown Riverside,

California, USA. The characteristics of the four LTE base

stations are summarized in Table VIII and their locations are

depicted in Fig. 9. The GPS receiver and LTE receiver clocks

were not synchronized, and the appropriate matrix B was

used (see Equation (6) in [5]). The red “X” signify locations

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Preprint of article accepted for publication in IEEE Transactions on Aerospace and Electronic Systems

Storage

USRP{2954R R©

IntegratedGNSS-IMU

Cellular antennas

(b) (c)

(a)

Fig. 8. Experimental setup. (a) Vehicle used to conduct the experiment,equipped with AsteRx-i V® GNSS-IMU module, antennas, USRP–2954R® ,and laptop for storage and processing. (b) Hardware setup mounted on top ofthe vehicle. (c) Hardware setup placed inside the vehicle.

where the vehicle was stationary for a few seconds, during

which the measurement noise variances and cellular clock bias

parameters were calculated.

TABLE VIIICHARACTERISTICS OF THE LTE BASE STATIONS

TowerService

provider

Carrier frequency

(MHz)Cell ID

Bandwidth

(MHz)

1 AT&T 1955 348-350 20

2 AT&T 1955 219 20

3 Verizon 2145 392 20

4 Verizon 2145 79 20

Cellular tower 1

Cellular tower 2

Cellular tower 4

Cellular tower 3

200 m

Fig. 9. Location of four cellular LTE base stations in downtown Riverside,California, USA whose signals were used. The red X’s signify locationswhere the measurement noise variances and cellular clock bias parameterswere calculated. This figure was obtained with ArcGIS® [14].

Three scenarios were considered. The first scenario com-

pares the experimental navigation performance (i.e., path

length, total RMSE, maximum eigenvalue, cost function)

versus the navigation performance predicted by the offline

path planning generator. Eight GPS satellites were present at

the time of the experiment and four LTE base stations were

used. Fig. 10 depicts the start and target points for the ground

vehicle. The path planning approach described in Section III

was executed offline with the settings in Table IX. It is worth

noting that cellular towers 1 and 3 were surrounded by tall

buildings. There are also tall buildings between tower 1 and 3

and the location where the measurement noise variances were

calculated (red X’s in Fig 9). It is suspected that this caused

the cellular measurement noise variances from towers 1 and 3

to higher than those from towers 2 and 4.

Because the Galileo constellation was not used in the

experimental study, the DOP and multipath-induced bias will

be higher compared to the simulation study, leading to higher

predicted constraint metrics. Therefore, to allow for feasible

paths, the constraints are relaxed in the experimental study.

Though this does not follow the rule for constraint selection

discussed in Subsection III-E1, the offline path planning gen-

erator output and experimental results can still be compared

as the settings used in each are identical. It should be noted

that in a realistic scenario, if the designer found that there

would be no feasible paths for the vehicle, a receiver for

another GNSS constellation (or additional sensors) can be

added, instead of adjusting the constraints. An experiment

with multiple GNSS constellations can be explored in future

work. The spacing between location indices where the position

MSE was generated was 8 meters. The LTE measurement

noise variances were calculated using the sample variance

from received pseudoranges, while the vehicle was stationary

over K = 100 samples. The perturbation parameters ǫm and

σ2ǫ,m were also calculated, while the vehicle was stationary

over K = 10 samples. The thresholds rmax and λmax are

relaxed compared to the simulation study because the Galileo

constellation is not used. The path planning generator returned

an optimal path and a feasible path depicted in Fig. 10.

The second scenario evaluates the navigation performance

if the vehicle chooses to take the shortest path (Path 3 in Fig.

10) instead of the optimal or feasible path. The settings for

Scenario 2 are identical to those in experimental Scenario 1.

The third scenario compares Approach A (does not account

for satellite motion) and Approach B (accounts for satellite

motion). A vehicle was driven along a long trajectory, which

was infeasible according to Approach A, but feasible ac-

cording to Approach B. The experimental results along this

path were compared to the offline path planning generator

output results from Approaches A and B. Table X provides

the settings for Scenario 3 that differ from Scenario 1.

B. Experimental Results

1) Scenario 1: The purpose of this scenario is to compare

the offline path planning generator output results with the

experimental navigation results. The vehicle was driven along

the optimal path, then the feasible path, and it was assumed

that the satellite geometry over the two paths did not change

drastically. The time difference between the two paths was 5minutes and 40 seconds, which is below the threshold time

7

Preprint of article accepted for publication in IEEE Transactions on Aerospace and Electronic Systems

for long trajectories (15 minutes). It was also confirmed that

there are no sharp changes in the GNSS reliability maps along

the path. Table XI compares the navigation performance (i.e.,

path length, total RMSE, maximum eigenvalue, cost function)

along the optimal and feasible paths returned by the simulated

results versus those returned experimentally.

Fig. 10. Path planning generator results: Path 1: optimal; Path 2: feasible;and Path 3: shortest between the start and target points, but is infeasible as itviolates the constraints. This figure was obtained with ArcGIS® [14].

TABLE IXEXPERIMENT SETTINGS FOR SCENARIOS 1 AND 2

Parameter Definition Value

N Number of satellites 8

MNumber of cellular base

stations4

t Start time (UTC)August 24, 2018,

6:34 am

rmax Position bias threshold 15 m

λmaxEigenvalue constraint

threshold30 m2

ηmaxPseudorange error

threshold2

√

10

KNumber of cellular

measurements used forinitialization

10

{σ2gnss,n}Nn=1

GNSS measurement noisevariance

{7.1, 5.1, 3.9,6.9, 7.1, 6.7,5.8, 9.5} m2

{σ2cell,m

}Mm=1

Cellular measurementnoise variance

{8.7, 4.4, 7.8,4.6}m2

Note the close match between the offline path planning

generator output and experimental navigation performance. In

particular, despite the differences in the offline path planning

generator output and experimental cost function values, Path 1

performed better than Path 2, as predicted by the path planning

generator.

The offline path planning generator output RMSEs at each

location are shown in Fig. 11. Also shown in Fig. 11 are the

vehicle’s ground truth path versus the experimentally estimated

TABLE XEXPERIMENT SETTINGS FOR SCENARIO 3

Parameter Definition Value

vAGV Vehicle speed 3.2 m/s

t Start time (UTC)December 26, 2018,

3:00 pm

{σ2gnss,n}Nn=1

GNSS measurement noisevariance

{7.7, 4.5, 5.6,7.2, 4.9, 9.0,8.6, 8.7} m2

TABLE XISCENARIO 1: OFFLINE PATH PLANNING GENERATOR OUTPUT RESULTS

(REFERRED TO AS SIMULATION) AND EXPERIMENTAL NAVIGATION

RESULTS ALONG OPTIMAL AND FEASIBLE PATHS

Path length Total RMSE

Path Simulation Experiment Simulation Experiment

Path 1: optimal 872 m 878 m 6.55 m 6.63 m

Path 2: feasible 884 m 886 m 7.19 m 7.47 m

Maximum eigenvalue Cost function value

Path Simulation Experiment Simulation Experiment

Path 1: optimal 27.91 m2 27.27 m2 55939 42216

Path 2: feasible 27.91 m2 26.85 m2 68688 60029

path with GPS and cellular LTE signals. It can be seen that the

offline path planning generator output RMSE closely follows

the experimentally estimated path.

Fig. 12 shows the offline path planning generator output

versus experimental position errors for (a) optimal and (b)

feasible paths. There are a few discrepancies between the

generated and experimental results, which could be attributed

to inaccuracies in the map. In one particular area of Fig. 11(b)

(depicted with a dashed circle), the experimental RMSE was

19.51 m, while the generated RMSE at that area was about 5m. This result can be seen in Fig. 12(b) (depicted with dashed

circles) from 108 s to 110 s. Note that the offline path planning

generator output RMSE increases to 17.01 m shortly thereafter.

There are also unexpectedly high experimental position errors

that do not match the generated RMSE from 41 s to 45 s. This

may be due to the fact that the offline path planning generator

does not account for attenuation due to trees (there was dense

foliage near both areas). This result reveals that accurate

knowledge of the environment could be crucial for accurately

generating the position MSE. The foliage was not included in

the 3-D map because it was not surveyed or available online

prior to the experiment. However, existing software packages

(e.g., Wireless Insite) could simulate foliage effects. There

are also areas in Fig. 12(b) where the offline path planning

generator output RMSE is larger than the experimental RMSE,

such as from 60 s to 80 s. This is a period of time where

the vehicle was stationary, and the actual measurement noise

variances may be smaller than the those calculated in the

initialization step. This can be addressed in future work by

parameterizing the measurement noise variances according to

the carrier-to-noise ratio (C/N0) instead of assuming it to be

constant.

8

Preprint of article accepted for publication in IEEE Transactions on Aerospace and Electronic Systems

(a)

(d)

(b)

(e)

Start point

RMSE < 5

5<RMSE<1010<RMSE<15

RMSE > 15

N=A

Estimated pathGround truth path

(c)

(f)

Target point Start point

Start point

Target pointTarget point

Path 1: Optimal Path 2: Feasible Infeasible path

Fig. 11. Offline path planning generator output results (referred to as simulated) and experimental results along (a),(d) optimal path; (b),(e) feasible path; and(c),(f) infeasible path. (a),(b),(c) show the simulated RMSE values at locations along the path, while (d),(e),(f) compare the vehicle’s experimentally estimatedpath from GNSS and cellular signals versus the ground truth path from the GNSS-IMU with RTK module. The dashed circle in (c) specifies the area in whichthe simulator did not have a sufficient number of measurements to estimate the vehicle’s position (corresponding to an RMSE of N/A), which matches thesame area in (f) at which there weren’t sufficient pseudorange measurements from GNSS and cellular signals to estimate the vehicles’s position. This figurewas obtained with ArcGIS® [14].

2) Scenario 2: This scenario evaluates the navigation per-

formance for a vehicle using Dijkstra’s path planning algo-

rithm to execute the path with the shortest length [28]. In

other words, the path planning algorithm does not account for

navigation performance: the cost function simply considers the

distance, while both constraints are removed. Path 3 in Fig.

10 is chosen which has a corresponding distance of 629 m

between the start and target points. As shown in Fig. 11 (c)

and (f), Path 3 was deemed infeasible by the path planning

generator as several areas had a simulated RMSE over 20 m,

and one area had an insufficient number of measurements to

produce an estimate of the vehicle’s state.

The experimental RMSE along the entire path was 12.12 m

in areas where the navigation solution was computed, which

is twice as large as the position RMSE of the other two paths.

The dashed circle depicted in Fig. 11(f) shows the area where

the vehicle was unable to estimate its position from GNSS

and cellular signals, which is consistent with Fig. 11(c). This

scenario highlights the importance of path planning to avoid

situations where the AGV could fail to estimate its state.

3) Scenario 3: This scenario compares the offline path

planning generator output navigation performances using Ap-

proach A and Approach B, and compares the results with

experimental data. The experimental data was collected along

a path that was infeasible according to Approach A but feasible

according Approach B. This path is shown in Fig. 13.

Table XII compares the navigation performance along this

path as returned by the offline path planning generator output

results versus those found experimentally.

TABLE XIISCENARIO 3: OFFLINE PATH PLANNING GENERATOR OUTPUT (REFERRED

TO AS SIMULATION) AND EXPERIMENTAL NAVIGATION RESULTS ALONG

THE CHOSEN PATH

DistanceTotal

RMSEMaximumeigenvalue

Cost

function

value

Experiment data 1187 m 5.78 m 27.93 m2 34890

Simulation data(Approach A)

1152 m 5.98 m 31.49 m2 35773

Simulation data(Approach B)

1152 m 5.94 m 29.19 m2 35369

It can be seen that the experimental results (total RMSE,

maximum eigenvalue, and cost function) agree more with

Approach B than Approach A. It should be noted that the

vehicle’s actual speed was nearly 6.7 m/s. These results

demonstrate an improvement in the path planning generator

when satellite motion is accounted for, even when the expected

vehicle speed is not exact. The experimental results also

show that the chosen path is feasible because it satisfies

the constraint, which is consistent with Approach B but not

consistent with Approach A. This shows that accounting for

GNSS satellite motion can lead to prescribed paths that are

shorter or have less error.

9

Preprint of article accepted for publication in IEEE Transactions on Aerospace and Electronic Systems

(b)

(a)

Fig. 12. Offline path planning generator output (referred to as simulated)position RMSE and experimental position error along (a) optimal path and(b) feasible path. Simulated position RMSE values are shown by red dots,while experimental position error is shown with blue dots.

Start point

Target point

Estimated path

Ground truth path

Fig. 13. The chosen path which is infeasible according to Approach A, andfeasible according to Approach B. Experimental results are shown of thevehicle’s estimated path from GNSS and cellular measurements. This figurewas obtained with ArcGIS® [14]

V. CONCLUSION AND FUTURE WORK

This paper considered the problem where an AGV equipped

with GNSS and cellular receivers desires to reach a target

location by taking the shortest path with minimum position

MSE, while guaranteeing that the bias in the position estimate

and the position uncertainty are below desired thresholds.

The prequel of this paper discussed algorithms to generate

signal reliability maps and path planning. This paper presented

simulation and experimental results demonstrating the efficacy

and accuracy of the path planning approach for several driving

scenarios. The simulation results revealed that the path plan-

ning approach (i) reduced the uncertainty about the AGV’s

position, (ii) increased the number of feasible paths to choose

from, which could be useful if other considerations arise

(e.g., traffic jams and road blockages due to construction),

and (iii) yielded significantly shorter feasible paths, which

would otherwise be infeasible with GNSS signals alone. The

experimental results carried out on a ground vehicle navigating

in downtown Riverside, California, USA, demonstrated a close

match with the simulated results.

The prescribed optimal path is expected to be among the

shortest paths in distance, while also accounting for position

accuracy along the path. Additionally, this path avoids areas

with large expected position errors, which could be violate

safety constraints. In some cases, the prescribed path may

avoid urban canyons altogether, and may direct the AGV

to leave the urban environment and re-enter closer to the

destination. In this case, it is recommended that the vehicle

manufacturer adds additional radio navigation receivers or

sensors to reduce the expected position error to meet safety

constraints. Other error sources can be introduced in the

path planning cost and constraints, such as GNSS multipath-

induced bias, or inaccuracies in the building footprints that

have been modeled in prior work [23]. Methods for GNSS

and cellular visibility predictions can be improved through

(1) comparing signal availability and received signal strength

to 3-D map predictions using power and shadow matching

[29]–[32], or (2) using a fish-eye camera to detect GNSS

NLOS [33], [34]. The same costs and constraints can be eval-

uated with different navigation frameworks that use filtering

techniques and sensor fusion. Integrity monitoring techniques

[35]–[39] and map matching [40]–[43] can also be used to

improve transmitter selection or augment the path planning

cost function. Time-varying path planning in approach B can

be improved by using traffic information [44].

ACKNOWLEDGMENT

The authors would like to thank Joe Khalife, Kimia

Shamaei, and Cody Simons for their help with data collection.

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